Harmonic Series
Like many theorists, Schenker began with the harmonic series. This is the series of harmonics (or overtones, or partials) that resonate when you play a given note. Here are the first 5 that sound when you play a C:

Number (fundamental labelled as 1)

Pitch

1

C

2

c (1 octave up)

3

g

4

c' (2 octaves up)

5

e'

6

g'

There are many more than this but, although contributing to timbre, there comes a point beyond which they cannot be heard. Not all correspond to notes of the western scale either - number seven for example is somewhere in between A and Bb. Schenker argued that only the first five were really audible and that together they made up the basic unit of tonal music - the triad (C, E and G). Schenker attributed almost mystical properties to this chord calling it the 'chord of nature'.

Schenker also pointed out that the first interval of the harmonic series (other than octave) is a rising fifth (from C to G). This is significant for two reasons:

Schenker argues that the harmonic series shows that the rising fifth is the basic motion of tonal music. This means that, after the tonic, the dominant is the most important chord. This makes sense when you consider the crucial function of the dominant in cadential progressions. Riemann, by contrast, proposes that the dominant and subdominant are equally important in the tonal system.

The rising fifth in the harmonic series is the reason that our key system is best understood in terms of what is called the circle of fifths.

Unlike some theorists who proposed highly complicated ways of deriving a minor triad from the harmonic series, Schenker suggested that the minor key system was essentially a man-made phenomenon - an alteration of the 'chord of nature' for expressive purposes.

You may be wondering what is dynamic about this system - are we not still talking about relationships? What is important (and where the fantasy comes in) is Schenker's explanation of the effect that these 'natural' phenomena have on the process of making music, as discussed in the next section.